Stability of stochastic partial differential equations with infinite delays

Abstract

In this paper, we study the existence and the asymptotical stability in p-th moment of mild solutions to stochastic partial differential equations with infinite delaysOur method for investigating the stability of solutions is based on the fixed point theorem.

Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks

“…In recent years, there is an increasing interest in stochastic functional differential equations due to their important applications in practice [1][2][3][4], and a large number of interesting results of these equations have been reported; see [5][6][7][8][9][10][11][12][13][14][15][16][17]. For instance, in 2002, Taniguchi et al [6] considered the existence, uniqueness, pth moment and almost sure Lyapunov exponents of mild solutions to a class of stochastic functional differential equations with finite delays by using semigroup methods.…”

Stability behavior of second order neutral impulsive stochastic differential equations with delay

“…Luo [18,17] have successfully applied fixed point principle to investigate the stability of mild solution of various stochastic equations. Luo and Taniguchi [19], have studied the asymptotic stability of neutral stochastic partial differential equations with infinite delay by using the fixed point theorem.…”

Mean square exponential stability for stochastic functional differential equations with impulses

“…For example, Taniguchi [13] has considered the exponential stability for stochastic partial differential equations by the energy inequality; Caraballo and Liu [9] have investigated the exponential stability for mild solution to stochastic partial differential equations with delays by utilizing the Gronwall inequality; Liu and Shi [6] have considered the exponential stability for stochastic partial functional differential equations by means of the Razuminkhin-type theorem; Taniguchi [11] has proved the almost sure exponential stability of mild solution for stochastic partial functional differential equation by using the analytic technique; Luo [4][5] has discussed asymptotic stability of stochastic partial differential equations with infinite delays and exponential stability for mild solutions of stochastic partial differential equation with delays by fixed point theorem, respectively.…”